Curmudge and Jaded Julie Talk about Models

(This is the continuation of a series of postings introduced on January 22, 2010.)

“Models, Curmudge? You mean those super-slender gals who look as if they have an eating disorder?”

“No, Jaded Julie. We’re going to talk about mathematical models; these are mathematical depictions of processes. Models were described in our discussions of queuing theory last July. Authors that we cited in Kaizen Curmudgeon a few weeks ago used models to forecast physician income in a medical home. We use value stream maps all the time as visual models to depict processes in the hospital. The equations that I learned in physics classes long ago were models of physical processes; they included statics (e.g., forces on a stationary beam), and dynamics (a ball rolling down an inclined plane).”

“Wow! There must be a model for everything. I’ll bet that the advent of the computer has made it possible to model processes that are more and more complex.”

“That’s for sure. We’ll talk more about that later, but let’s start by considering a very simple example. Our daughter moved to a new house in Madison, so I consulted MapSeek* to learn how to get there. In addition to directions, MapSeek said that our daughter’s house is 104.61 miles from ours and that it would take us 1 hour and 54 minutes to get there. In computing our travel time, MapSeek must have used the model, time equals distance divided by an estimated average speed. Their average speed was 55 mph (104.61 miles ÷ 1.9 hours).”

“I’m with you, Curmudge. Because the MapSeek routing uses Highway 26, their average speed must have been adjusted for slowing down in Rosendale to avoid getting a speeding ticket and perhaps also for the possibility of getting stuck behind a farmer pulling a load of manure on 26, a two-lane highway. But is the best route now using Highway 26 through Rosendale? U.S.-151 is now four lanes all the way from Fond du Lac to Madison. Perhaps we should give this new information to MapSeek so they can adjust their model.”

“That would certainly seem to be the proper thing to do, Julie. But let’s consider this hypothetical case. Suppose the MapSeek people own a coffee shop in Rosendale. They wouldn’t want to change their recommended route and their model because it would hurt their coffee shop’s business. That’s called having a vested interest in their model and the data that go into it. MapSeek would prefer that we shut up about there being a better route; perhaps they might even try to suppress all discussions of alternate ways to go from Appleton to Madison.”

“Hey, that’s not fair! We all depend on MapSeek for the correct information.”
“It’s a sad story, Julie. We can see through what Mapseek might do because it’s hard to color the results from a simple, transparent model based on a classical equation. In addition, Mapseek’s work can be easily tested empirically. But when a bunch of suspect data are poured into a complex computer model that is arcane, abstruse, and tentative, anything can happen. That is especially true when someone has a vested interest in the outcome.”

“(Although Curmudge uses words that are known to only a few people and are hard for the rest of us to understand, I get the picture.) Hey, Curmudge, your story is a parable, isn’t it? May I explain its lesson?”

“Go ahead, but don’t get too specific.”

“Think critically. Be slow to accept the conclusions of investigators attempting to model a complex process when their work is supported—even indirectly—by people with a vested interest in their results.”

*Our apologies to MapQuest for using a name similar to theirs in this totally hypothetical example.